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This paper presents numerical and experimental validation of results obtained by a shell finite element, which has been developed for modeling of the dynamic behavior of sandwich multilayered structures with a viscoelastic core. The proposed shell finite element is very easy to implement in existing finite element solvers, since it uses only the displacements as degrees of freedom at external faces and at inter-layer interfaces. The displacement field is linearly interpolated in the thickness direction of each layer, and analytical integration is made in the thickness direction in order to avoid meshing of each sandwich layer by solid elements. Only the two dimensional mid-surface of reference is meshed, facilitating the mesh generation task. A simplified modal approach using a real modal basis is also proposed to efficiently calculate the dynamic response of the sandwich structure. The proposed method reduces the memory size and computing time and takes into account the frequency-dependence of the polymer core mechanical properties. Results obtained by the proposed element in conjunction with the simplified modal method have been numerically and experimentally validated by comparison to results obtained by commercial software codes (MSC/NASTRAN and ESI/RAYON-VTM), and to measurements done on automobile windscreens.

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The dynamic response of a laminated windshield with a viscoelastic core is computed using a simplified modal method combined with a quadratic sandwich finite element. The method is based on a modal expansion of the displacement field using a constant young modulus of the core layer. The frequency dependence of the complex modulus of the core is taken into account using the residual dynamic stiffness matrix. The method is applied to predict the frequency response of two types of laminated windshield using a standard and acoustic PVB cores. Numerical results are compared in a first step with those obtained using the direct solver of Nastran software, and in a second step with experimental results obtained by a laser vibrometer. Comparisons show a very good agreement between experimental and numerical results and demonstrate the efficiency of the simplified modal solving method and the developed parabolic sandwich element. The method will be applied to compute the coupled vibro-acoustic frequency response of a full vehicle body integrating a laminated windshield and glass surfaces.

SUMMARY This paper presents a non‐isoparametric shell finite element, which is very easy to implement in a finite element solver, for modelling of sandwich multilayered structures with a viscoelastic core. The proposed shell finite element uses only the displacements at external faces and at interlayer interfaces. Linear and quadratic variations of the displacements are assumed in the transverse direction of each layer. Exact numerical integration of the elementary stiffness and mass matrices are carried out along the thickness direction of each layer to avoid generation of solid meshes. Hence, only a 2D finite element mesh of the midsurface of the sandwich is needed, facilitating the mesh generation task. The developed shell finite element was used to calculate natural frequencies and normal modes of a car's windscreen, and associated frequency response has been computed using a simplified modal solving approach, which reduces the memory size and computing time. The simplified modal approach takes into account the frequency dependence of the mechanical properties of the polymer core. Results obtained with the developed shell element are in good agreement with those obtained using 3D hexahedral solid elements (H20) available in I‐DEAS (Siemens PLM Software, Plano, TX, USA) and Nastran (Siemens PLM Software, Plano, TX, USA) software codes. Copyright © 2012 John Wiley & Sons, Ltd.